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\begin{equation*}\sin \frac{7\pi}{60} = \sin 21^\circ = \frac{2 \sqrt{5 - \sqrt 5} \left( \sqrt 3 + 1 \right) - \sqrt 2 \left( \sqrt 3 - 1 \right) \left(1 + \sqrt 5 \right)}{16}\end{equation*}
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